5+ e6z dx = %3D 4e3z Select one: a. None of these b. pe 31 edz 12 C. 12 C - 12 d. 교e 3z +C 12 12

Q: a) FVoa = ? PMT - 300 r= e 4%=0.04, Az0.04 12 2 0•00333 %3D 5x 12 z 60

A: According to the given information, it is required to rewrite the answer. For part(a)

Q: %3D 니e?. H(t-1) + et.8t-4)

A:

Q: d'y Given: y = ax + bx³ + cx² + dx + e, where a, b, c, d, e are constant, find dx5

A: Topic:- derivatives

Q: d3y +6° dx2 d²y d- dx3 15 dy 15 dx 100y = 0 - - %3D

A: Given :d3ydx3+6d2ydx2-15dydx-100y=0

Q: If 3f(x)dx 6, and 5f(x)dx 15 ,then 6f(x)dx: %3D %3D %3D (a) 10 (b) 20 (c) 30 (d) 0 (e) 40

A: We have to find the integral

Q: 2x If y= e, then %3D dx² a. 2x O b. 6e²x 2x 4e²* Od. 2e²*

A:

Q: d²y -4 If x? + y? = 4 then show that dx?

A: By simply differentiate  with respect to x to find d^2y/dx^2

Q: Q1. Evaluate by substitution method 2 e*dx 1 – e2x |

A:

Q: 8. If x = 1- 1 and y = In 1, what is in terms of 1 ? dx (B) 21 (C) -- (A) (D) 212 (E) 214

A: Given x=t2-1,  y=lntdxdt=2t,  dydt=1t Now,  dydx=dydtdxdt=1t2t=12t2

Q: if dx =3 then k =2e3 %3D - Select one: True False

A:

Q: Determine whether the statement is true or false. If it is false, explain why or give an example…

A: For a function y(x), the quantity dydx represents the first derivative of y. This quantity…

Q: Obtain the GS of: 2 (Згу — 4у + 6) dz + (23 — ва? ? — 1) dy %3D 0 - a. x³y – 2x?y3 + 3x² b. x3у —…

A:

Q: L. Given 2+ 2r + br - 19z +15 - cx + dx? + ex +f, find the values of b, c, d, e and f. * + 2r +5 INP…

A:

Q: dx Cane:2e-25x

A: 13)

Q: C) d4 器 ★竹+ s×M 3. %3D +2x 4. If ap diffelentiat e with les Pectto Subject. 1 / 7 l

A: given,        y=x44+2x2

Q: Q2) If y(0) = 0 and y'(0) = 0, ƒ (t) = e*t, %3D 1 y(t) = (D + 3)(D + 2)(D + 1)ƒ (t), determine y(t).…

A: Here first calculate differential part.

Q: Given y = u28 and u = 5– 3x?, find dy/dx. A. = 168x(5 - 3x?)27 D. dx = -28x(5 – 3x²)²7 dx dy В. dx…

A: As we know that; The Power law: ddxxn=nxn-1 The Quotient rule: fg'=f'·g-g'·fg2   (1). Given: y=u28…

Q: 522 – 7z+3 dz - 12 dt 15w – 13u? + w dw f) e) d)

A:

Q: Solve the following diffential eauations a) dy + 4 y = e dy 3n2y = そ? ea3 dy C) N + 2y = そマ dn

A: We need to solve DE.

Q: dy Find the general solution for: -6y dx Select one: O y=C.e¯z О у y = C. e-6x O y = e-6x O None. O…

A:

Q: d²y Compute dz? at the point (1, 2) given a² – y² = -3. a) 3 b) 4 9 d) 8 e) O

A:

Q: 2f(x)dx = - 4 and | (F(x) + 1)dx =7. Then | (3f(x) – 2x)dx = Select one: а. -2 b. 19 С. 10 d. 13

A: ∫-122f(x)dx=-4 and ∫-13(f(x)+1)dx=7. find ∫23(3f(x)-2x)dx

Q: 80. If x? – y? = 1, find d²y/dx² at the point (2, V3).

A: Given: x2-y2=1 at 2,3

Q: dy If x2 + y? = 13, then at dx the point (2, 3) is : -3 2 -2 3 -4 3

A: x2+y2=13 differentiate with respect to x, 2x+2ydydx=02ydydx=-2xdydx=-xy

Q: 3. If f f(x)dx = 7, then , (2f(x) + 5) dx = %3D %3D (A) 14 (В) 19 (C) 24 (D) 29 (E) 57

A: Integration.

Q: The solution of dy dx 2xy = x2 + 3y? when y(1) = 3 23 + 10y3 = a? a3 + y = 10x2 Option 1 Option 2 23…

A:

Q: i-p if x2 + 3y2 = 10. Find dx? Select one: За — 2у? 4x?y + y³ а. - 3+ 2x°y2 + y² 2x4 – 3xy2 Ob. 2a4…

A: Given that: x2+3y2=10

Q: d Find dx - (12t8 +2020)dt. 1 4 +2020x + C а. 3 12x8 - 12 Ob. 8' 12x° + 2020 Oc. None of the other…

A:

Q: d?y Find , if y = (60)tª + csc (5t2- e10t) + In (2t² + 3) dt2

A: To Determine: find d2ydt2 Given: we have y=60t4+cosec5t2-e10t+ln2t2+3 Explanation: we have to…

Q: d²y if 2x2 + 5y² = 9. Find %3D dx2 Provide your answer below: -口 dy dx2

A:

Q: Seve: dy %3D e A Be

A:

Q: f (x) dx=6, ƒ (x) dx=2, and ƒ (x) dx=- 3, fir If A 4 B

A: We are asked to find the value of given.

Q: t = b? Choose 1 answer: b Ⓒ / ° v A a © B Ⓒ a b cb a a b e20t+t6 dt e10t+t³ dt 10e10t+ 3t² dt…

A: Topic = Integration

Q: Consider the diagram below. d/ r 12 If mzr = 37°, which of the following is the measure of Ls. %3D A…

A: We have to find angle

Q: dy Find dx Assume a, b, and c are constants. ,3 (a) x² + y³ = 8 2 (b) ax² – by? = c². -

A: Differentiation problem

Q: J(y) = S. [(2x – 3)²y? – 6y²] dæ, - 3)²y2 – 6y²] dx, Y € C²[a,b] Find

A: Given:

Q: f of If dx + In(7y), what is ? - дхду Select one: 1 7. а. дхду y y b. дхду - y + 7e?y С. дхду 1+e7y…

A: Option E is correct.  Make x constant

Q: e. (3х — 2у?)dx —- 2хydy %3D 0

A:

Q: D Frnef far s ? syf 2=7

A: You must have idea how to solve the equation. The explanation part is given below.

Q: 5. For what value of k, k> 0, does (6kx-2k) dx = -k³ ? о 1 02

A:

Q: Solve by substitution of u = Ax + By +C  dy/dx = (x + y +3)2

A:

Q: dy If y = (x- 1) e* then dx2 %3D O A.

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: 16z dV, where E is the upper hemisphere of x? + y² + 2² = 1

A: We have to find the value of the given triple integral ∫∫∫E16z dV where E is the upper hemisphere…

Q: dy If y = e4a+19 then dx

A:

Q: d) Given a and r = -5, calculate S6. 2 e) Given tn = 3tn-1+2 and t4 = (-2), find ts.

A: Solution

Q: Q4 Find y'of y = In- %3D ? 1+e0

A:

Q: Jad dy If x = t³ – 1 and y = 3e*, then %3D dx A) B) t2 C) et 3e D) 3t2 – 1

A:

Q: Q6: Solve the following Higher-Order D.E. d³y d²y dy + 7- 5y = 0 dx 3 %3D - dx3 dx2 To find the…

A: